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Optimal asymptotic quadratic error of density estimators for strong mixing or chaotic data


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  • Bosq, Denis
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    Under mild mixing conditions, we show that the kernel density estimator has exactly the same asymptotic quadratic error as in the i.i.d. case. Curiously, that result remains almost valid if the data are chaotic.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 22 (1995)
    Issue (Month): 4 (March)
    Pages: 339-347

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    Handle: RePEc:eee:stapro:v:22:y:1995:i:4:p:339-347

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    Keywords: Density estimation Optimality Mixing Chaos;


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    1. Vieu, Philippe, 1991. "Quadratic errors for nonparametric estimates under dependence," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 324-347, November.
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    Cited by:
    1. N. Hosseinioun & H. Doosti & H. Nirumand, 2012. "Nonparametric estimation of the derivatives of a density by the method of wavelet for mixing sequences," Statistical Papers, Springer, vol. 53(1), pages 195-203, February.
    2. Biau, Gérard, 2002. "Optimal asymptotic quadratic errors of density estimators on random fields," Statistics & Probability Letters, Elsevier, vol. 60(3), pages 297-307, December.
    3. D. Blanke & D. Bosq & D. Guégan, 2003. "Modelization and Nonparametric Estimation for Dynamical Systems with Noise," Statistical Inference for Stochastic Processes, Springer, vol. 6(3), pages 267-290, October.


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